How does the Projected (2D) mode of the Proportional Editing works?
To explain it, here's an example of Connected mode. I'm pulling one vertex on the right side view of the image. Notice the effect on the left screen: it works like the standard mode for proportional editing, the vertices within the influence circle will be transformed proportionally. 



On Projected 2D mode, doing the same action results in a transformation of all the vertices aligned on the view and within the circle.